For an optional ungraded assignment (see it as a complex problem that wont be graded, more to test our skills and knowledge) I was given the following problem. It is not as straightforward as all the other examples we covered and I would really like to know how to solve the problem.
A hotel is estimating that in the next 7 days they will need to have available the following number of sheets:
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Sheet demand | 20 | 15 | 30 | 40 | 45 | 45 | 15 |
Starting day 1 they have 0 sheets. They need to buy sheets at $20 per set and they can wash to reuse. There are 2 types of laundry services:
$6 requiring 2 days (sheets can be used on day 1 and then again on day 3)
$3 requiring 3 days (sheets can be used on day 1 and then again on day 4)
The question:
How can I formulate the linear programming model to determine the optimal laundry and purchasing policy? And how can I run this using Gurobi (Python)?
I am absolutely stumped and truly don't know how to tackle the problem. All help will be much appreciated, but if not possible also not a huge deal.